D-analogues of q-shifted factorial and the q-Kummer sum

TL;DR

This paper introduces D-analogues of q-series, including q-binomial coefficients and the q-Kummer sum, extending hypergeometric q-series concepts into the Dirichlet series framework.

Contribution

It develops the theory of D-analogues for q-binomial coefficients and the q-Kummer sum, providing new tools for Dirichlet series analysis.

Findings

Defined D-analogues of q-binomial coefficients

Established D-analogue of the q-Kummer sum

Extended hypergeometric q-series concepts into Dirichlet series domain

Abstract

Recently, the concept of a D-analogue was introduced by the author. This is a Dirichlet series analogue for the already known and well researched hypergeometric q-series. we consider the D-analogues of the q-binomial coefficients, and a D-analogue of the q-Kummer (Bailey-Daum) sum.